INSTRUCTOR: In this screencast,
I'm gonna describe the first law
of thermodynamics for a closed system,
so important we understand
what we mean by a closed system.
This means that there's no mass
transferring across the system boundaries,
so whatever mass we start with at time zero,
we have the exact same mass in the system at a later time.
Also, since we're interested in applying
the first law to chemical engineering type problems,
we're gonna ignore kinetic energy,
and in fact the things fluids moving inside the system,
and we're also gonna ignore potential energy.
So the first law then in differential form
says the change in internal energy U is internal energy,
the heat transfer some differential time
when we're looking at the change in internal energy,
work where we're talking about expansion compression work,
and we'll talk a little more about this,
and then work, talking about shaft work.
So let's make sure these terms.
This is heat transfer across the boundary,
so we define our system
and if temperature one inside the system
and temperature two outside the system,
and temperature two for example
is greater than temperature one,
we have heat transfer in this direction,
and so the sign notation is important
if we have heat transfer the way I've indicated,
Q going into the system, Q is positive
adding energy to the system, it's positive.
For expansion compression work,
what we're looking at is where we have
for example, a piston cylinder arrangement,
and say we have a gas a here,
and we're pushing down on this piston,
so we're doing work by pushing down,
so, in that case, this is expansion compression work,
work's greater than zero the way I've drawn it,
again we're adding energy.
Shaft work would mean, for example,
we had a system with an impeller inside
and this impeller is rotating,
adding energy to the fluid inside this system
again the work, shaft work would be positive.
We're adding energy to the system.
Now if we look at the integrative form of the first law
where delta U change in internal energy
between initial and the final state,
Q plus work for expansion compression,
work for shaft work, and now this term,
expansion compression work is minus integral
pressure external, in other words,
when pushing down, it's this pressure
that determines the work for pushing down
or it's pushing the gas is expanding and pushing up,
the negative sign is here because
if the volume decreases,
so this were negative,
then the work would be positive,
and that's what we looked at here
is the work is positive if we're compressing a gas.
If it's reversible, and we'll talk elsewhere
other screencasts what mean by that,
then this expansion compression work
is integral minus other pressure
of, for example, the gas inside the system,
but only if it's reversible that
we can use the pressure in here.
Otherwise, this is external pressure
that is used in our calculation work.
So one common one might be a constant pressure process,
and then delta u, again we're talking about closed system,
Q constant pressure we can bring outside the intergral sign,
and I'm going to write this
as constant pressure and reversible,
so this is the pressure for example
with a gas inside delta V,
and I'm doing the case where the shaft work is zero,
and so I can rearrange this because pressure's constant
I can put it inside this delta sign,
and then I can bring that term
to the other side of the equation,
and our definition now of enthalpy is U plus PV,
so the left side is delta H,
so delta H equals Q if we have a closed system,
constant pressure, and reversible.
The other case would be constant volume,
so a fixed volume container.
This means there's no expansion compression work,
and so delta U equals Q.
Now, let's look at both these cases for constant pressure,
if we had an ideal gas, delta H is Cp delta T
constant heat capacity ideal gas,
Cp delta T is equal to Q.
Here if we have an ideal gas delta u
is Cv delta T is equal to Q.